Enigma Number 1543

Pentagony

From a point inside a pentagon I have drawn lines (all of different lengths of less than 25 centimetres) to its five corners. The lines and the sides of the pentagon are all whole numbers of centimetres long. Furthermore, all five angles at the point are whole numbers of degrees, and none is a right angle.

How long is the perimeter of the pentagon?

WIN £15 will be awarded to the sender of the first correct answer opened on Wednesday 3 June. The Editor’s decision is final. Please send entries to Enigma 1543, New Scientist, Lacon House, 84 Theobald’s Road, London WC1X 8NS, or to enigma@newscientist.com (please include your postal address).

Answer to 1537 A name game&colon; Paul’s magic square did not contain the letters of his name

The winner John Woolhouse of Sheffield, UK

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